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# Calculus 1A: Differentiation

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### Overview

How does the final velocity on a zip line change when the starting point is raised or lowered by a matter of centimeters? What is the accuracy of a GPS position measurement? How fast should an airplane travel to minimize fuel consumption? The answers to all of these questions involve the derivative.

But what is the derivative? You will learn its mathematical notation, physical meaning, geometric interpretation, and be able to move fluently between these representations of the derivative. You will discover how to differentiate any function you can think up, and develop a powerful intuition to be able to sketch the graph of many functions. You will make linear and quadratic approximations of functions to simplify computations and gain intuition for system behavior. You will learn to maximize and minimize functions to optimize properties like cost, efficiency, energy, and power.

The three modules in this series are being offered as an XSeries on edX. Please visit Single Variable Calculus XSeries Program Page to learn more and to enroll in the modules.

This course was funded in part by the Wertheimer Fund.

*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.

### Syllabus

Abridged Syllabus

Limits

1. Limit Laws
2. Continuity
3. Intermediate Value Theorem

Differentiation

1. Introducing the Derivative
2. Rules for differentiation of all known functions
3. Approximations

Applications of Differentiation

1. Curve Sketching
2. Optimization
3. Related Rates

David Jerison

## Reviews

5.0 rating, based on 7 Class Central reviews

Start your review of Calculus 1A: Differentiation

• Ivan Z
Very detailed and comprehensive to the point where it's not possible not to understand concepts or not to be able to solve challenging problems. We are all very fortunate that Professor Jerison and his team spent the time to put together this experience for us. I suspect that it's on an ongoing effort where changes are being made to facilitate learning. It is very rewarding. It can be time-consuming, but I finally realized that to really get math, it takes this much time and effort. Third course in the sequence in at this point, the only thing I am missing is more MIT math MOOCs.
• -Must for everyone!!!
Good:
-Short videos
-Concept explaination
-Short quizz really tests your knowledge AWESOME :)
-Limits are explained in a great way.
-Why this course is not self paced?
• A fantastic course.

Everything about the course is top-notch. Short and clear videos, plenty of challenging and relevant exercises, innovative interactive exercises and active support from staff in the forums.
• Dna47a
An excellent course from MIT. Can't describe it but you have to take it to experience how good the course materials are.
• Anonymous
All of the materials are excellent! Very nice pedagogy and comprehensive. Really hope to see more courses from the math department of MITX.
• Marat Minshin
• Max Friedrich

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